Area of a Circle Segment Given the Central Angle
Definition: The number of square units it takes to fill a
segment of a circle
Try this Drag one of the orange dots that define the endpoints of the segment.
Note the number of square units it takes to fill it.
The formula to find the area of the segment is given below. It can also be found by calculating the area of
the whole pieshaped sector and subtracting the area of the
isosceles triangle △ACB.
Where:
C 
is the central angle in DEGREES 
R 
is the radius of the circle of which the segment is a part. 
π 
is Pi, approximately 3.142 
sin 
is the trigonometry Sine function. 
If you know the segment height
If you know the segment height and radius of the circle you can also find the segment area. See
Area of a Circular Segment given the Segment Height.
Calculator
Use the calculator below to calculate the segment area given the radius and segment's central angle, using the formula described above
Remember: In this version, the central angle must be in degrees.
Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
(C) 2009 Copyright Math Open Reference. All rights reserved
